Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  vector<long long> v;
  map<long long, bool> cek;
  for (long long i = 1; i * (i + 1) / 2 <= 1e9; i++) {
    v.push_back(i * (i + 1) / 2);
    cek[i * (i + 1) / 2] = 1;
  }
  long long x;
  cin >> x;
  for (long long i = 0; i < v.size(); i++) {
    if (cek[x - v[i]]) return cout << "YES\n", 0;
  }
  cout << "NO\n";
}